15-Dec-84 23:20:47-EST,3587;000000000001
Date: Saturday, 24 November 1984 16:46-EST
Sender: John R. Kender
From: John R. Kender
Orig-To: BBOARD at COLUMBIA-20.ARPA
Subject: The imperceptibility of Santa Claus
ReSent-From: CARTER@RU-BLUE.ARPA
ReSent-To: Info-Cobol@MC
ReSent-Date: Sat 15 Dec 1984 23:12-EST
"OK, Daddy, why has nobody SEEN Santa Claus on Christmas Eve?" Tough
question. But, a few back-of-the-envelop calculations were enough to
convince my doubting offspring that it was physically IMPOSSIBLE. To
wit:
Suppose that Santa starts at the International Date Line and travels
westward, in order to maximize his time for delivering presents on or
about midnight. Let's guess that there are 4 billion people, and so
about 1 billion households worldwide. Just as we assume Santa has
solved the travelling salesman problem (1 billion nodes!), so too we
will assume that he can handle the unequal distribution of households
over the land masses, too (Fiji Islanders, etc., probably don't have
reason to doubt his presence). Roughly 1 billion / 24 hours gives 40
million households / hour; and as there are 3600 seconds / hour, that
gives us about 10000 households / second. Thus, Santa drops down the
chimney and is gone, on average in .0001 second: FAR LESS time than
the human eye (even dark-adapted!) needs to see--.01 second being
about the lower limit established by tachistoscope studies.
"OK, Daddy, then why has nobody HEARD Santa Claus on Christmas Eve?"
Tougher question, and one that demands serious analysis. If Santa
moves that quickly, of course, he is going to push a lot of air out of
his way, and silent night would be more accurately be called the Night
of the Sonic Booms. The envelop (last year's, once containing a
Christmas card as yet unanswered) quickly fills up:
Let's see: 1 billion households distributed on average equally over 4
pi radius squared. That's about 12 times 4000 * 4000, but
three-quarters of that is water (poor Fiji!): so about 3 times 16
million, or about 50 million square miles. So, 1 billion / 50 million
is 20 households / square mile, and if they were distributed in
gridlike regularity, Santa has to travel (at LEAST, depending on the
sophisication of his TSP solution) about 1/5 mile: 1000 feet in .0001
second. Sound itself would take about 1.3 second; clearly, even if
Santa were made of Kevlar and could withstand the accelerations
necessary (poor toys!), Santa is not only booming about the Baby
Boomers' babies, he is beginning to suffer from Fitzgerald
contraction. (Let's see, here on the envelop flap: 1/5 mile in
1/10000 of a second is 2000 miles / second, or about .01c, if c is
rounded to 200000 miles / second.) Thus giving new meaning to
"relative clause", he is approaching the danger of being misperceived
as anorexic.
Perhaps, then, the answer is as follows: you can't see Santa because
he moves too fast; and, because he would look skinnier than you think,
you wouldn't recognize him anyway. Further, any atmosphere
overpressure generated by his rapid descent is canceled by the
underpressure of his nearly instantaneous return: in contrast to most
phenomena, the sonic boom cannot form!
What remains to be explained, of course, in addition to the usual
arrival of undamaged gifts (even on Fiji), is why the evening of his
rapid transit is not marked by the spectacle of a multitide of gifts
being sucked, nearly simultaneously, up through millions of chimneys
throughout world, to trail happily in his wake.